FormulasFinalfinal_paper_2_advanced_fmChapter 2
Back to Chapters

Chapter 2

Topics and formulas

Filter by Topic

All Formulas

20 formulas

Weighted Average Cost of Capital (WACC)

Topic: Business ValuationChapter: Chapter 2
WACC=(EV)×Ke+(DV)×Kd×(1−T)WACC = \left( \frac{E}{V} \right) \times K_e + \left( \frac{D}{V} \right) \times K_d \times (1 - T)
WACC represents the average rate of return a company expects to pay to its investors. It is used as the discount rate for Free Cash Flow to Firm (FCFF) in DCF valuation. E is the market value of equity, D is the market value of debt, V is the total market value of the firm (E+D), K_e is the cost of equity, K_d is the cost of debt, and T is the corporate tax rate.

Capital Asset Pricing Model (CAPM) for Cost of Equity (K_e)

Topic: Business ValuationChapter: Chapter 2
Ke=Rf+β×(Rm−Rf)K_e = R_f + \beta \times (R_m - R_f)
CAPM is used to calculate the cost of equity, which is the return required by equity investors. R_f is the risk-free rate, \beta (beta) is the systematic risk of the equity, and (R_m - R_f) is the market risk premium.

Free Cash Flow to Firm (FCFF)

Topic: Business ValuationChapter: Chapter 2
FCFF=EBIT×(1−T)+Depreciation−Capital  Expenditure−ΔWorking  CapitalFCFF = EBIT \times (1 - T) + Depreciation - Capital\;Expenditure - \Delta Working\;Capital
FCFF represents the total cash flow generated by a company before any debt payments but after all operating expenses and reinvestments. It is used to value the entire firm. EBIT is Earnings Before Interest and Taxes, T is the corporate tax rate, and \Delta Working;Capital is the change in net working capital.

Terminal Value (Gordon Growth Model)

Topic: Business ValuationChapter: Chapter 2
TV=FCFFt+1WACC−gTV = \frac{FCFF_{t+1}}{WACC - g}
Terminal Value represents the value of a company's cash flows beyond the explicit forecast period, assuming a stable growth rate. FCFF_{t+1} is the Free Cash Flow to Firm in the first year after the explicit forecast period, WACC is the Weighted Average Cost of Capital, and g is the perpetual growth rate of FCFF.

Enterprise Value (using DCF)

Topic: Business ValuationChapter: Chapter 2
EV=∑t=1nFCFFt(1+WACC)t+TV(1+WACC)nEV = \sum_{t=1}^{n} \frac{FCFF_t}{(1 + WACC)^t} + \frac{TV}{(1 + WACC)^n}
Enterprise Value is the total value of a company, including both equity and debt, derived by discounting all future FCFFs and the Terminal Value back to the present. FCFF_t is the Free Cash Flow to Firm in year t, WACC is the Weighted Average Cost of Capital, and n is the number of years in the explicit forecast period.

Economic Value Added (EVA)

Topic: Business ValuationChapter: Chapter 2
EVA=NOPAT−(Capital  Invested×WACC)EVA = NOPAT - (Capital\;Invested \times WACC)
EVA measures a company's true economic profit by subtracting the cost of capital from its Net Operating Profit After Tax (NOPAT). A positive EVA indicates value creation. NOPAT is EBIT \times (1 - T), Capital;Invested is the total capital employed by the business, and WACC is the Weighted Average Cost of Capital.

Exchange Ratio (based on EPS)

Topic: Business ValuationChapter: Chapter 2
Exchange  Ratio=EPSAcquirerEPSTarget×P/ETargetP/EAcquirerExchange\;Ratio = \frac{EPS_{Acquirer}}{EPS_{Target}} \times \frac{P/E_{Target}}{P/E_{Acquirer}}
The exchange ratio determines how many shares of the acquiring company's stock a target company's shareholder will receive for each of their shares. This formula calculates the ratio based on relative P/E ratios and EPS, aiming for a fair exchange. EPS is Earnings Per Share, and P/E is the Price-to-Earnings ratio.

Post-Merger Earnings Per Share (EPS)

Topic: Business ValuationChapter: Chapter 2
Post  Merger  EPS=(EPSAcquirer×SharesAcquirer)+(EPSTarget×SharesTarget)±Synergy  BenefitsSharesAcquirer+(SharesTarget×Exchange  Ratio)Post\;Merger\;EPS = \frac{(EPS_{Acquirer} \times Shares_{Acquirer}) + (EPS_{Target} \times Shares_{Target}) \pm Synergy\;Benefits}{Shares_{Acquirer} + (Shares_{Target} \times Exchange\;Ratio)}
This formula calculates the combined EPS after a merger or acquisition, considering the earnings of both companies, potential synergy benefits, and the new total number of shares outstanding. It helps determine if the merger is EPS accretive or dilutive. Synergy;Benefits should be after-tax.

Price-to-Earnings (P/E) Ratio

Topic: Business ValuationChapter: Chapter 2
P/E  Ratio=Market  Price  Per  ShareEarnings  Per  ShareP/E\;Ratio = \frac{Market\;Price\;Per\;Share}{Earnings\;Per\;Share}
The P/E ratio is a widely used relative valuation metric that compares a company's current share price to its per-share earnings. It indicates how much investors are willing to pay for each rupee of earnings. It's used to compare companies within the same industry.

Enterprise Value to EBITDA (EV/EBITDA) Ratio

Topic: Business ValuationChapter: Chapter 2
EV/EBITDA  Ratio=Enterprise  ValueEarnings  Before  Interest,  Taxes,  Depreciation,  and  AmortizationEV/EBITDA\;Ratio = \frac{Enterprise\;Value}{Earnings\;Before\;Interest,\;Taxes,\;Depreciation,\;and\;Amortization}
The EV/EBITDA ratio is another popular relative valuation multiple that compares the total value of a company (Enterprise Value) to its operating cash flow (EBITDA). It's often preferred over P/E for comparing companies with different capital structures or depreciation policies.

Exchange Ratio (Shares based on Market Price)

Topic: Mergers and AcquisitionsChapter: Chapter 2
Exchange Ratio=Market Price per Share of Acquired CompanyMarket Price per Share of Acquiring Company\text{Exchange Ratio} = \frac{\text{Market Price per Share of Acquired Company}}{\text{Market Price per Share of Acquiring Company}}
This formula determines the number of shares of the acquiring company offered for each share of the acquired company, based on their respective market prices. It is a common method for structuring share-for-share acquisitions.

Exchange Ratio (Shares based on EPS and P/E)

Topic: Mergers and AcquisitionsChapter: Chapter 2
Exchange Ratio=EPS of Acquired CompanyEPS of Acquiring Company×P/E Ratio of Acquiring CompanyP/E Ratio of Acquired Company\text{Exchange Ratio} = \frac{\text{EPS of Acquired Company}}{\text{EPS of Acquiring Company}} \times \frac{\text{P/E Ratio of Acquiring Company}}{\text{P/E Ratio of Acquired Company}}
This formula calculates the exchange ratio considering the earnings per share (EPS) and price-to-earnings (P/E) ratios of both companies, aiming to maintain a certain EPS or P/E parity post-merger.

Earnings Per Share (EPS) after Merger

Topic: Mergers and AcquisitionsChapter: Chapter 2
EPSpost-merger=Total Earnings of Combined EntityTotal Number of Shares of Combined Entity\text{EPS}_{\text{post-merger}} = \frac{\text{Total Earnings of Combined Entity}}{\text{Total Number of Shares of Combined Entity}}
This formula calculates the earnings per share for the combined entity after the merger. It is critical for assessing whether the merger is EPS accretive (increases EPS) or dilutive (decreases EPS) for the acquiring company's shareholders.

Market Price per Share (MPS) after Merger

Topic: Mergers and AcquisitionsChapter: Chapter 2
MPSpost-merger=EPSpost-merger×P/Epost-merger\text{MPS}_{\text{post-merger}} = \text{EPS}_{\text{post-merger}} \times \text{P/E}_{\text{post-merger}}
This formula projects the market price per share of the combined entity, assuming a certain post-merger P/E ratio is applied to the new EPS. The post-merger P/E can be the acquirer's P/E, target's P/E, or a blended P/E.

Synergy Value (using Present Values)

Topic: Mergers and AcquisitionsChapter: Chapter 2
Synergy Value=PV of Expected Post-Merger Cash Flows−(PV of Acquirer’s Cash Flows+PV of Target’s Cash Flows)\text{Synergy Value} = \text{PV of Expected Post-Merger Cash Flows} - (\text{PV of Acquirer's Cash Flows} + \text{PV of Target's Cash Flows})
This formula quantifies the additional value created by combining two companies, which is greater than the sum of their individual values. Synergy can arise from cost savings, revenue enhancements, or tax benefits, and is calculated as the present value of the incremental cash flows.

Cost of Acquisition (Share Exchange)

Topic: Mergers and AcquisitionsChapter: Chapter 2
Cost of Acquisition=Number of Shares Issued by Acquirer×Market Price per Share of Acquirer\text{Cost of Acquisition} = \text{Number of Shares Issued by Acquirer} \times \text{Market Price per Share of Acquirer}
This formula calculates the total cost incurred by the acquiring company when the consideration for the target company is paid by issuing its own shares. The market price of the acquirer's shares at the time of acquisition is used.

Value of Firm (Free Cash Flow to Firm - FCFF Valuation)

Topic: Mergers and AcquisitionsChapter: Chapter 2
Value of Firm=∑t=1nFCFFt(1+WACC)t+Terminal Value(1+WACC)n\text{Value of Firm} = \sum_{t=1}^{n} \frac{\text{FCFF}_t}{(1 + \text{WACC})^t} + \frac{\text{Terminal Value}}{(1 + \text{WACC})^n}
This formula values the entire firm by discounting its Free Cash Flows to the Firm (FCFF) at the Weighted Average Cost of Capital (WACC). FCFF represents the cash flow available to all capital providers (debt and equity).

Value of Equity (Free Cash Flow to Equity - FCFE Valuation)

Topic: Mergers and AcquisitionsChapter: Chapter 2
Value of Equity=∑t=1nFCFEt(1+Cost of Equity)t+Terminal Value(1+Cost of Equity)n\text{Value of Equity} = \sum_{t=1}^{n} \frac{\text{FCFE}_t}{(1 + \text{Cost of Equity})^t} + \frac{\text{Terminal Value}}{(1 + \text{Cost of Equity})^n}
This formula values the equity portion of the firm by discounting its Free Cash Flows to Equity (FCFE) at the cost of equity. FCFE represents the cash flow available to equity holders after all expenses and debt obligations.

Economic Value Added (EVA)

Topic: Mergers and AcquisitionsChapter: Chapter 2
EVA=NOPAT−(Capital Invested×WACC)\text{EVA} = \text{NOPAT} - (\text{Capital Invested} \times \text{WACC})
EVA measures a company's true economic profit by deducting the cost of capital from its Net Operating Profit After Tax (NOPAT). A positive EVA indicates that the company is creating value for its shareholders above the cost of capital.

Net Present Value (NPV) of Merger

Topic: Mergers and AcquisitionsChapter: Chapter 2
NPVmerger=Value of Combined Firm−(Value of Acquirer+Cost of Acquisition)\text{NPV}_{\text{merger}} = \text{Value of Combined Firm} - (\text{Value of Acquirer} + \text{Cost of Acquisition})
This formula calculates the net benefit or cost of a merger from the acquiring company's perspective. A positive NPV indicates that the merger is expected to create value for the acquiring company's shareholders.
Chapter 2 Formulas — CA Final | Kartavvya